The perimeter of a triangle with two equal sides is 71 cm. if its base were lengthened by 6 cm and each leg were shortened by 4 cm, all three sides would be equal. find the length of the base of the original triangle.

Your answer would be 17cm.

Because two sides are equal, we can label these two sides x, and the base y, and since the perimeter is 71cm, we can then write the equation 2x + y = 71.

Then we apply the changes made to our sides, so the two equal sides would become x - 4, and the base would become y + 6. We can now set these equal to each other as it states that all sides are equal when this change occurs.

Now we have a pair of simultaneous equations that we can solve with substitution firstly by rearranging the equation x - 4 = y + 6 to get x:

x - 4 = y + 6

+ 4

x = y + 10

Now we can substitute (y + 10) as x into the equation 2x + y = 71 :

2(y + 10) + y = 71

2y + 20 + y = 71

3y + 20 = 71

- 20

3y = 51

÷ 3

y = 17

I hope this helps!

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